{
  "id": "2002.09210",
  "version": "v1",
  "published": "2020-02-21T10:32:28.000Z",
  "updated": "2020-02-21T10:32:28.000Z",
  "title": "An algorithm for computing the $Υ$-invariant and the $d$-invariants of Dehn surgeries",
  "authors": [
    "Taketo Sano",
    "Kouki Sato"
  ],
  "comment": "38 pages, 5 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "By using grid homology theory, we give an explicit algorithm for computing Ozsv\\'ath-Stipsicz-Szab\\'o's $\\Upsilon$-invariant and the $d$-invariant of Dehn surgeries along knots in $S^3$. As its application, we compute the two invariants for all prime knots with up to 11 crossings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-21T10:32:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M25"
    ],
    "keywords": [
      "dehn surgeries",
      "grid homology theory",
      "prime knots",
      "explicit algorithm",
      "computing ozsvath-stipsicz-szabos"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}